One more level and your Braxien will evolve into Delphox, and then it will learn Mystical Fire. Replace Flame Charge with Mystical Fire. You probably want to replace Fire Spin with something for coverage. If you have access to the Move Tutor, I'd recommend Shockwave to deal with Water types, or Signal Beam to deal with Dark types. You could also go with TM 99 for Dazzling Gleam for Dark types, with the added benefit of dealing with Dragons quite nicely. You might want to consider replacing Psyshock as well, but there are reasons to keep it alongside another Psychic attack.
Since you already have/are about to have a powerful Psychic special attacker, you don't really need a second one. Replace the Kirlia with something else. If it were male, you could have maybe kept it to become a Gallade instead, but you're still doubling up on Psychic type doing that.
Given its current level, Ivysaur looks pretty decent. I'd definitely replace Poison Powder with Toxic. It's a much stronger status, and works equally well with Venoshock. The evolutionary line favors special attacks, rather than physical ones, so you should be looking to replace Razor Leaf and Vine Whip to that end. If you were breeding for things, I'd do Giga Drain personally, for the sustain it brings. But that's an Egg Move, not a TM, so that may not be in the cards for your present time. A good alternative is Energy Ball from TM 53. Or you could use Solar Beam, with or without Sunny Day.
Your Lopunny only knows 3 moves? Or maybe you just missed one... Either way, I'm personally not a fan of Jump Kick (or High Jump Kick). There are other options you can use. Foresight is easy to replace. With.... anything, really. Personally Normal types aren't that interesting to use on a team.
Inkay/Malamar are more of a manipulator type of Pokemon, which can be incredibly powerful in PvP. Just playing through the story, though... there's little point. Once you get your team past about level 40, the only opponents that should pose any real threat to you are Gym Leaders, the E4, and the story's evil team boss. And even then, leverage type advantages and you're fine. The simple fact is that the random trainers you will encounter don't have any strategy in how they play, and as such, a Pokemon that manipulates based on that strategy (like Inkay/Malamar) is honestly a lot of wasted effort. That's not to say that you can't use them, by any means. But you'd be better off for the purposes of the story just assembling a team of heavy hitters that cover as many types as possible. With that in mind, I'd replace Inkay with something like Bisharp or Mawile.
Your Honedge looks solid to me. Just be aware that when you do eventually evolve it to Aegislash that it is the definition of a glass cannon. You will have to "stance dance" appropriately with it's signature move, King's Shield, if you do ever need to take a hit.